Arithmetic Geometry

Arithmetic Geometry

For thirty years, the biennial international conference AGC^2T (Arithmetic, Geometry, Cryptography, and Coding Theory) has brought researchers to Marseille to build connections between arithmetic geometry and its applications, originally highlighting coding theory but more recently including cryptog...

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Bibliographic Details
Main Author: Aubry, Yves
Other Authors: Howe, Everett W., Ritzenthaler, Christophe
Format: eBook
Language:English
Published: Providence : American Mathematical Society, 2019.
Series:Contemporary Mathematics Ser.
Subjects:
Coding theory > Congresses.
Geometry, Algebraic > Congresses.
Cryptography > Congresses.
Number theory > Congresses.
Coding theory
Cryptography
Geometry, Algebraic
Number theory
Conference papers and proceedings
Online Access:Click for online access
Table of Contents:
  • Cover; Title page; Contents; Preface; Hasse-Witt and Cartier-Manin matrices: A warning and a request; Prologue; 1. Matrices and semilinear algebra; 2. Hasse-Witt and Cartier-Manin matrices; 3. Cartier-Manin matrices for hyperelliptic curves; 4. Hasse-Witt matrices through the ages; 5. Subsequent developments; 6. Conclusion; References; Works that cite Manin (1961) or Yui (1978); Analogues of Brauer-Siegel theorem in arithmetic geometry; Introduction; 1. Classical Brauer-Siegel theorems; 2. Zeta and -functions; 3. Abelian varieties and surfaces; 4. Generalisations
  • 5. Theorems and conjectures of Brauer-Siegel typeReferences; The Belyi degree of a curve is computable; 1. Introduction; Acknowledgements; 2. The Belyi degree; 3. First proof of Theorem 1.2; 4. Second proof of Theorem 1.2; 5. The Fermat curve of degree four; References; Weight enumerators of Reed-Muller codes from cubic curves and their duals; 1. Introduction; 2. Singular projective plane cubic curves; 3. Smooth projective plane cubic curves; 4. Low-weight coefficients of _{ _{2,3}^{\perp}}(,); 5. Singular affine plane cubic curves; 6. Smooth affine plane cubic curves
  • 7. Low-weight coefficients of _{(^{ }_{2,3})^{\perp}}(,)8. Acknowledgments; References; The distribution of the trace in the compact group of type ₂; 1. Introduction; 2. Exponential sums; 3. The group \Gtwo and its Lie algebra; 4. Real forms; 5. The Steinberg map of \Gtwo; 6. Maximal torus and alcove of \UGtwo; 7. The Steinberg map on \UGtwo; 8. The Weyl integration formula revisited; 9. Image of the alcove; 10. Distribution of the trace; 11. Moments; References; The de Rham cohomology of the Suzuki curves; 1. Introduction
  • 2. The de Rham cohomology as a representation for the Suzuki group3. The Dieudonné module and de Rham cohomology; 4. An explicit basis for the de Rham cohomology; References; Décompositions en hauteurs locales; 1. Introduction; 2. Présentation des décompositions; 3. Hauteurs globales, hauteurs locales; 4. Modèles de Moret-Bailly des variétés abéliennes; 5. Hauteur d'un point par la formule clef; 6. Décomposition de la hauteur de Faltings d'une jacobienne hyperelliptique; 7. Calculs explicites en dimension 1; \frenchrefname; Using zeta functions to factor polynomials over finite fields
  • 1. Introduction2. Schoof's algorithm; 3. Kayal's factoring idea; 4. Pila's algorithm; 5. Generalization of Kayal's factoring idea; 6. A heuristic for Hypothesis Z; 7. Weakening Hypothesis Z; 8. Using varieties other than abelian varieties; Acknowledgements; References; Canonical models of arithmetic (1; ∞)-curves; 1. Uniformizations and orders; 2. \Belyi maps; 3. Canonical models; 4. Modular interpretations; References; Maps between curves and arithmetic obstructions; 1. Introduction; 2. The fundamental group; 3. Certifying non-isomorphism; 4. Examples

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